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HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

arXiv 2102.02515 ↗First posted 4 Feb 2021cs.LGcited by 38

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Abstract (arXiv)

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HYDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HYDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HYDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra_8686.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 49 of its 61 references that are in the map. First posted on arXiv 4 Feb 2021.

Builds on

49 of 61 references.

References · 49

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37 more
  1. 2014Striving for Simplicity: The All Convolutional Netcited by 983
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  14. 2017Deep Learning is Robust to Massive Label Noisecited by 164
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  16. 2019On the Accuracy of Influence Functions for Measuring Group Effectscited by 146
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Citing papers per year: 2021: 5; 2022: 5; 2023: 8; 2024: 7; 2025: 12; 2026: 1.

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  5. 2021Rethinking Influence Functions of Neural Networks in the Over-parameterized Regimecited by 26
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  7. 2022Adapting and Evaluating Influence-Estimation Methods for Gradient-Boosted Decision Treescited by 16
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  8. 2024Overcoming Catastrophic Forgetting by Exemplar Selection in Task-oriented Dialogue Systemcited by 3
  9. 2025Unraveling Indirect In-Context Learning Using Influence Functionscited by 3
  10. 2025ExPLAIND: Unifying Model, Data, and Training Attribution to Study Model Behaviorcited by 3
  11. 2025Understanding Data Influence with Differential Approximationcited by 3
  12. 2021Augment & Valuate : A Data Enhancement Pipeline for Data-Centric AIcited by 2
  13. 2024Fast Training Dataset Attribution via In-Context Learningcited by 2
  14. 2025Fast-DataShapley: Neural Modeling for Training Data Valuationcited by 2
  15. 2025UtilGen: Utility-Centric Generative Data Augmentation with Dual-Level Task Adaptationcited by 2
  16. 2026LoRIF: Low-Rank Influence Functions for Scalable Training Data Attributioncited by 2
  17. 2023Representer Point Selection for Explaining Regularized High-dimensional Modelscited by 1
  18. 2024Which Experiences Are Influential for RL Agents? Efficiently Estimating The Influence of Experiencescited by 1
  19. 2025Conversational Explanations: Discussing Explainable AI with Non-AI Expertscited by 1
  20. 2021Longitudinal Distance: Towards Accountable Instance Attributioncited by 0
  21. 2023Which Experiences Are Influential for Your Agent? Policy Iteration with Turn-over Dropoutcited by 0
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